In a vacuum, a photon travels faster because it travels at light speed, which electrons cannot reach.
It is possible for electrons in a medium to travel faster than photons. In water, for example, high-energy electrons can travel at speeds faster than photons. Cherenkov radiation may result, which can be easily detected as visible light. This radiation is used in neutrino detectors. In these detectors, there is a large amount of water. The occasional collision between a high energy neutrino and an electronic can accelerate the latter beyond the speed of light.